Let A, B be sets with |A| = m n = |B|, and let a(m, n)

Question:

Let A, B be sets with |A| = m ‰¥ n = |B|, and let a(m, n) count the number of onto functions from A to B. Show that
a(m, 1) = 1

when m ‰¥ n > 1.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 08:44 AM

See More Questions

a. Let A = {1, 2, 3, 4, 5, 6, 7} and B = {v, w, x, y, z}. Determine the number of functions /: A B where (i) f(A) = {v, x}; (ii) |f(A)| = 2; (iii) f(A) = {w, x, y}; (iv) If(A) | = 3; (v) f(A) = {u,...
The rooted Fibonacci trees Tn, n ¥ 1, are defined recursively as follows: (1) T1 is the rooted tree consisting of only the root; (2) T2 is the same as T1 - it too is a rooted tree that consists...
Let X1, . . . , Xn" be a random sample from a continuous population whose median is denoted by M. For testing H0: M = M0, we can use the sign test statistic S = No. of Xi > M0,i = 1, . . . , n. H0 is...
If r = (t, t 2 , t 3 ), find r(t) and r(t).
Use the multistep process to interpret the regression results below. This model has been run by a researcher trying to explain customer loyalty to a restaurant. The independent variables are customer...
The plane rectangular gate can pivot about the support at B. For the conditions given, is it stable or unstable? Neglect the weight of the gate. Justify your answer with calculations. Water 8 m Gate...
What are the final two steps a researcher should do after presenting the research findings to the decision makers?
Phelps Company distributed the following dividends to its stockholders: (a) 450,000 shares of Bedrock Corporation stock, carrying value of investment, $975,000; fair market value, $1,350,000. (b)...
Could I obtain assistance with these . problems? 1. Find the coordinates of the turning points of the curve y=3x^4-8x^3-30x^2+72x+5. Determine the nature of these points. "Determine the nature"...
Qwert Typewriter Company and Yuiop Typewriters, Inc., are identical except for capital structures. Qwert has 50 percent debt and 50 percent equity financing, whereas Yuiop has 20 percent debt and 80...
Let n,k Z+, and define p(n, k) to be the number of partitions of n into exactly k (positive-integer) summands. Prove that p(n, k) = p(n - 1), (k - 1) + p(n - k, k).
When one examines the units digit of each Fibonacci number Fn, n 0, one finds that these digits form a sequence that repeats after 60 terms. [This was first proved by Joseph-Louis Lagrange...
Assume that on December 31, 2018, Stora Enso (FIN) signs a 10-year, non-cancelable lease agreement to lease a storage building from Sheffield Storage. The following information pertains to this lease...
Since Ruth's primary goal is not to make an exorbitant profit, how low could her annual net operating cash flows be and still generate a 5% return (i.e., a zero NPV)? State this annual amount in...
QUESTION 8 Year 2 Year 1 For the year ended December 31 $8,500 $6,500 Revenues Expenses Net Income 5,500 4,000 At December 31 Year 2 Year 1 Assets $15,500 $9,000 Liabilities Stock Retained Earnings...
5. Kassi Handover purchased as small caf in a northern Texas town with $600,000 of her own money. Help her prepare her T accounts for her first month of operations using the information provided...
Florence Lighting Inc. has to raise some cash using debt financing. The board of directors is discussing what terms and conditions would be appropriate for this new debt issue. They need some...
. Assume that consumers in a nation reduce their marginal propensity to save from 0.25 to 0.2 though their personal incomes initially do not change. How will this change in MPS affect the economy?...
The following selected accounts appear in Zimmerman Company's unadjusted trial balance at December 31, 2018, the end of its fiscal year (all accounts have normal balances). Additional information is...
During the year land was revalued and the surplus reported as Revaluation surplus; and an asset costing 80,000, written down to 38,000, was sold for 40,000. Identify the cost of any non-current...
If Q is an n ( n matrix such that the angles (Qx, Qy) and (x, y) are equal for all vectors x and y in , prove that Q is an orthogonal matrix.
W is the line in with general equation 2x - 5y = 0 IR2
Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector space. If it is not, list all of the axioms that fail to hold. The set of...
1. Electric potential is given by V=6x-8xy-8y+6yz - 4z Then magnitude of electric force acting on 2C point charge placed on origin will be :- (1) 2N (2) 6N (3) 8N (3) 8N (4) 20 N 2. Figure shows...
17. A concave mirror produces a real image 10mm tall, of an object 2.5mm tall placed at 5cm from the mirror. Calculate focal length of the mirror and the position of the image. 18. An object is...
23. A convex mirror used for rear view on an automobile has a radius of curvature of 3m. If a bus is located at 5m from this mirror, find the position, nature and magnification of the image. 24. An...

Let A, B be sets with |A| = m n = |B|, and let a(m, n)

Question:

Il a(m, n) = nm

Step by Step Answer:

Let B n 1 and A m Then f A B where fa b for all a A and b B is the only o...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions